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Joined 1 year ago
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Cake day: July 2nd, 2023

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  • from a topological perspective, wraps and tacos are two different beasts.

    in a wrap, the bread completely surrounds (and encloses) the other ingredients, so theres a 2-dimensional hole involved (which basically means the inside is hollow).

    in a taco, no such wholes are present.

    you can also distinguish sandwiches from tacos and wraps (since sandwiches involve two pieces of bread, like you said). but unfortunately, you can’t topologically distinguish a burger from a sandwich


  • it is possible to rigorously say that 1/0 = ∞. this is commonly occurs in complex analysis when you look at things as being defined on the Riemann sphere instead of the complex plane. thinking of things as taking place on a sphere also helps to avoid the “positive”/“negative” problem: as |x| shrinks, 1 / |x| increases, so you eventually reach the top of the sphere, which is the point at infinity.



  • i think this is a fairly reasonable gut reaction to first hearing about the “unnatural” numbers, especially considering the ways they’re (typically) presented at first. it seems like kids tend to be introduced to the negative numbers by people saying things like “hey we can talk about numbers that are less 0, heres how you do arithmetic on them, be sure to remember all these rules”. and when presented like that, it just seems like a bunch of new arbitrary rules that need to be memorized, for seemingly no reason.

    i think there would be a lot less resistance if it was explained in a more narrative way that explained why the new numbers are useful and worth learning about. e.g.,

    • negative numbers were invented to make it possible to subtract any two whole numbers (so that it’s possible to consistently undo addition).
    • rational numbers were invented to make it possible to divide any two whole numbers (so that it’s possible to consistently undo multiplication, with 0 being a weird edge-case).
    • real numbers were invented to facilitate handling geometrical problems (hypotenuse of a triangle, and π for dealing with circles), and to facilitate the study of calculus (i.e. so that you can take supremums, limits, etc)
    • complex numbers were invented to make it possible to consistently solve polynomial equations (fundamental theorem of algebra), and to better handle rotations in 2d space (stuff like Euler’s formula)

    i think the approach above makes the addition of these new types of numbers seem a lot more reasonable, because it justifies the creation of all the various types of numbers by basically saying “there weren’t enough numbers in the last number system we were using, and that made it a lot harder to do certain things”


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    toMemes@lemmy.mlIt all makes sense now
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    2 months ago

    it’s mathematically provable that the shortest path between any two points on a sphere will be given by a so-called “great circle”. (a great circle is basically something like the equator: one of the biggest (greatest) circles that you can draw on the surface of a sphere.) i think this is pretty unintuitive, especially because this sort of non-euclidean geometry doesn’t really come up very frequently in day to day life. but one way to think about this that on the sphere, “great circles” are the analogues of straight lines, although you’d need a bit more mathematical machinery to make that more precise.

    although in practice, some airlines might choose flight paths that aren’t great circles because of various real world factors, like wind patterns and temperature changes, etc.



  • its so tiresome to have all these services constantly made worse. these days it feels whenever a new thing comes out, it has about two or three years before it’s run into the ground in pursuit of the almighty dollar.

    and this kind of thing is also happening to movies/tv shows/video game franchises. it feels like no matter how good it starts, you only get (at most) 2 or 3 sequels before the executives get their hands on it and run it into the ground. sure there are exceptions to this, but they are few and far between. and its becoming even more common for shows/video games to simply disappear if the parent company decides to remove them from online stores/streaming platforms.

    all around, it just feels like things are becoming less and less permanent




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    2 months ago

    they’re probably assuming it will be like every skyrim update released in the past 10 years, which is a fair assumption.

    and this update has also caused the widely anticipated fallout london project being indefinitely postponed. in the article linked, you can see the fallout london project lead saying:

    “But with the new update dropping just 48 hours [after Fallout London’s original release date], the past four years of our work stand to just simply break.”

    i don’t really see what good it does to say “nobody can know that at this time”, when people have every reason to think that it will break their mods. i mean sure, nobody knows the future, but you can say that about literally every single prediction made about anything in the future. it’s a tautology. are you trying to imply people shouldn’t make predictions about anything?